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Pier Operator (Posted on 2008-12-13) Difficulty: 2 of 5
Substitute each of the letters by a different decimal digit from 0 to 9 to satisfy this alphametic square root extraction problem. None of O and P can be 0.

                P I E R
  --------------------
√ O P E R A T O R |
   C T
------------
      B E R
      B A C
------------------
         E  P A T
         T  I A  I
----------------------
             P I  E O R
             P I  E O R
----------------------

Note: Try to derive a non computer assisted method, although computer program/spreadsheet solutions are welcome.

See The Solution Submitted by K Sengupta    
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Solution Without knowing the whole square-root algorithm (computer assisted soln) | Comment 1 of 2
A computer program that considers only whether PIER^2 = OPERATOR yields:

4975          24750625
5061          25613721

but the second one is ruled out as P*P would be OP, rather than the different CT shown.

OPERATOR is therefore 24750625, while
PIER is 4975.

And C is 1 and B is 24-16 = 8.

Thus, one need not know the entire square-root algorithm.

DEFDBL A-Z
FOR p = 1 TO 9
IF had(p) = 0 THEN
 had(p) = 1
FOR o = 1 TO 9
IF had(o) = 0 THEN
 had(o) = 1
FOR i = 0 TO 9
IF had(i) = 0 THEN
 had(i) = 1
FOR e = 1 TO 9
IF had(e) = 0 THEN
 had(e) = 1
FOR r = 0 TO 9
IF had(r) = 0 THEN
 had(r) = 1
FOR a = 0 TO 9
IF had(a) = 0 THEN
 had(a) = 1
FOR t = 1 TO 9
IF had(t) = 0 THEN
 had(t) = 1

 pier = p * 1000 + i * 100 + e * 10 + r
 operator = o * 10000010 + p * 1000000 + e * 100000 + r * 10001 + a * 1000 + t * 100
 IF pier * pier = operator THEN PRINT pier, operator

 had(t) = 0
END IF
NEXT
 had(a) = 0
END IF
NEXT
 had(r) = 0
END IF
NEXT
 had(e) = 0
END IF
NEXT
 had(i) = 0
END IF
NEXT
 had(o) = 0
END IF
NEXT
 had(p) = 0
END IF
NEXT

Note the program considers that E and T are also non-zero in keeping with the spirit of such things, though the same two possibilities are supplied even if zero is allowed for these two variables.

  Posted by Charlie on 2008-12-13 19:24:34
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